On the global well-posedness of the one-dimensional Schrodinger map flow

TL;DR

This paper proves the global well-posedness of the Schrödinger map flow for certain domain and target manifolds, advancing understanding of its mathematical properties and partially resolving a longstanding conjecture.

Contribution

It establishes the global well-posedness of the Schrödinger map flow from the real line into Kähler manifolds and from the circle into Riemann surfaces, addressing a conjecture by W.-Y. Ding.

Findings

Proves global well-posedness for maps from the real line into Kähler manifolds.

Establishes global well-posedness for maps from the circle into Riemann surfaces.

Partially resolves Ding's conjecture on Schrödinger map flow.

Abstract

We establish the global well-posedness of the initial value problem for the Schrodinger map flow for maps from the real line into Kahler manifolds and for maps from the circle into Riemann surfaces. This partially resolves a conjecture of W.-Y. Ding.